According to this data (Section: Kapp'n, Subsection: Details) we would have to permanently stay in the future.Yes, the rare island types are time locked until you reach a certain date in-game for each island with your character. For people who've been playing the game for over a year (or TT'd so their island was created over a year before the in-game date), this isn't an issue, but in your case you wouldn't see most of these rare island types for months.